You haven’t really responded to her arguments though which is potentially why she doesn’t understand.
this is a classic problem actually.
If I say no, and give you a reason, that does not mean that you can solve my reason and then it will be a yes.
I see this a lot on mn, in both directions.
either - you didn't give a clear NO, you just gave reasons, so they thought that if they could solve the issues, then it would be fine.
or - like here, you haven't explained yourself, so they haven't heard NO.
We do need to learn that when someone says no, they mean no. They will give you a reason, which is a courtesy/politeness thing, it is not a list of obstacles that you then need to break down.
It is not unreasonable to ask - eg - no because of your dog; you ask - if I found somewhere else for dog would that make a difference? But once you have been told no, you should assume it means no.
And as the person saying no, it is fine to stick to your guns.